\[ \left (-2 \left (x^2-1\right ) (\mu (\mu +1)+\nu (\nu +1))+24 x^3-8\right ) y''(x)-6 x (\mu (\mu +1)+\nu (\nu +1)-2) y'(x)+\left ((\mu (\mu +1)-\nu (\nu +1))^2-2 \mu (\mu +1)-2 \nu (\nu +1)\right ) y(x)+\left (x^2-1\right )^2 y^{(4)}(x)+10 x \left (x^2-1\right ) y^{(3)}(x)=0 \] ✗ Mathematica : cpu = 86.1436 (sec), leaf count = 0
DSolve[(-2*mu*(1 + mu) - 2*nu*(1 + nu) + (mu*(1 + mu) - nu*(1 + nu))^2)*y[x] - 6*(-2 + mu*(1 + mu) + nu*(1 + nu))*x*Derivative[1][y][x] + (-8 + 24*x^3 - 2*(mu*(1 + mu) + nu*(1 + nu))*(-1 + x^2))*Derivative[2][y][x] + 10*x*(-1 + x^2)*Derivative[3][y][x] + (-1 + x^2)^2*Derivative[4][y][x] == 0,y[x],x]
, DifferentialRoot result
\[\left \{\left \{y(x)\to (x)\right \}\right \}\]
✓ Maple : cpu = 0.345 (sec), leaf count = 35
dsolve((x^2-1)^2*diff(diff(diff(diff(y(x),x),x),x),x)+10*x*(x^2-1)*diff(diff(diff(y(x),x),x),x)+(24*x^2-8-2*(mu*(mu+1)+nu*(nu+1))*(x^2-1))*diff(diff(y(x),x),x)-6*x*(mu*(mu+1)+nu*(nu+1)-2)*diff(y(x),x)+((mu*(mu+1)-nu*(nu+1))^2-2*mu*(mu+1)-2*nu*(nu+1))*y(x)=0,y(x))
\[y \left (x \right ) = \left (\LegendreQ \left (\mu , x\right ) c_{2}+c_{1} \LegendreP \left (\mu , x\right )\right ) \LegendreP \left (\nu , x\right )+\LegendreQ \left (\nu , x\right ) \left (\LegendreQ \left (\mu , x\right ) c_{4}+c_{3} \LegendreP \left (\mu , x\right )\right )\]